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October 20, 2014

Homework Help: Math: Calculus

Recent Homework Questions About Calculus

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Calculus Help Please!!! Check
A curve passes through the point (0, 2) and has the property that the slope of the curve at every point P is three times the y-coordinate of P. Find an equation of the curve. dy/dp = 3y or ∫ (3/y) dy = ∫ dp or 3 ln(y) = p + c or @ (0,2) ln(2) = 0 + c or c = ln(2) 3...
Wednesday, April 2, 2014 at 4:39pm

calculus help thanks!
The gas law for an ideal gas at absolute temperature T (in kelvins), pressure P (in atmospheres), and volume V (in liters) is PV = nRT, where n is the number of moles of the gas and R = 0.0821 is the gas constant. Suppose that, at a certain instant, P = 8.0 atm and is ...
Wednesday, April 2, 2014 at 4:35pm

Calculus Help Please!!!
A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 40 cm/s. Find the rate at which the area within the circle is increasing after each of the following. after 1 s = after 3 s = after 7 s =
Wednesday, April 2, 2014 at 4:32pm

Calculus Help Please!!!
Consider the following. f(x) = 8x (square root of (x − x^2)) (a) Use a graph to find the absolute maximum and minimum values of the function to two decimal places.
Tuesday, April 1, 2014 at 10:27pm

Calculus Help Please!!!
Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 2x^2 − 5x + 1, [0, 2] If it satisfies the hypotheses, find all numbers c that satisfy the conclusion of the Mean Value Theorem. (Enter your answers as a comma-separated list...
Tuesday, April 1, 2014 at 10:08pm

Calculus Help Please!!!
Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = xe^((−x^2)/98), [−6, 14]
Tuesday, April 1, 2014 at 9:14pm

Calculus Help Please!!!
Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = (t square root of (64 − t^2)) ,[−1,8]
Tuesday, April 1, 2014 at 9:11pm

Calculus Help!
Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = xe^(−x^(2)/98), [−6, 14]
Tuesday, April 1, 2014 at 9:09pm

Calculus
Find the absolute minimum and absolute maximum values of f on the given interval. f(t) = 8 cos t + 4 sin 2t, [0, π/2]
Tuesday, April 1, 2014 at 5:45pm

Calculus Help Please!!!
Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = (t square root of (64 − t^2)), [−1, 8]
Tuesday, April 1, 2014 at 5:27pm

Calculus Help Please!!!
Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 2x^3 − 3x^2 − 72x + 7 , [−4, 5]
Tuesday, April 1, 2014 at 5:26pm

calculus and vectors
Determine an equation of the line of intersection of the planes 4x − 3y − z = 1 and 2x + 4y + z = 5.
Tuesday, April 1, 2014 at 4:59pm

calculus
Twenty feet wire is used to make two figures? What is the maximum areas of enclosed figures.
Tuesday, April 1, 2014 at 11:14am

Calculus
Find the area cut off by x+y=3 from xy=2. I have proceeded as under: y=x/2. Substituting this value we get x+x/2=3 Or x+x/2-3=0 Or x^2-3x+2=0 Or (x-1)(x-2)=0, hence x=1 and x=2 are the points of intersection of the curve xy=2 and the line x+y=3. Area under curve above X axis ...
Tuesday, April 1, 2014 at 3:07am

Calculus
The circle defined by the equation x^2 + y^2 = 18 has two points where the slope of its tangent line is m=1. Find those points.
Monday, March 31, 2014 at 11:41am

Calculus: Integral
I don't understand how to do this one integral problem that involves secant. I'm asked to find the integral of sec^4 (4x). I'm not really sure how to go about solving this problem.
Monday, March 31, 2014 at 3:32am

Calculus Help Please!!!
Verify the given linear approximation at a = 0. Then determine the values of x for which the linear approximation is accurate to within 0.1. (Enter your answer using interval notation. Round your answers to three decimal places.) fourth root of (1 + 2x)≈ 1 + (1/2)x
Sunday, March 30, 2014 at 11:21pm

Calculus Help Please!!!
The circumference of a sphere was measured to be 80 cm with a possible error of 0.5 cm. 1) Use differentials to estimate the maximum error in the calculated volume. (Round your answer to the nearest integer.) 2) What is the relative error? (Round your answer to three decimal ...
Sunday, March 30, 2014 at 11:17pm

Calculus Help
Use differentials to estimate the amount of paint needed to apply a coat of paint 0.03 cm thick to a hemispherical dome with diameter 54 m. (Round your answer to two decimal places.)
Sunday, March 30, 2014 at 11:16pm

Calculus Help Please
Use a linear approximation (or differentials) to estimate the given number. (1.999)^4
Sunday, March 30, 2014 at 10:14pm

Calculus Help Please!!!
Compute Δy and dy for the given values of x and dx = Δx. (Round your answers to three decimal places.) y = 3x − x^2, x = 3, Δx = −0.6 Δy=???
Sunday, March 30, 2014 at 9:57pm

Calculus Help Please!!!
Verify the given linear approximation at a = 0. Then determine the values of x for which the linear approximation is accurate to within 0.1. (Enter your answer using interval notation. Round your answers to three decimal places.) ln(1 + x) ≈ x xE
Sunday, March 30, 2014 at 8:28pm

Calculus Help Please!!!
Two carts, A and B, are connected by a rope 39 ft long that passes over a pulley P (see the figure). The point Q is on the floor h = 12 ft directly beneath P and between the carts. Cart A is being pulled away from Q at a speed of 3.5 ft/s. How fast is cart B moving toward Q at...
Sunday, March 30, 2014 at 7:16pm

Calculus Help Please!!!
A water trough is 5 m long and has a cross-section in the shape of an isosceles trapezoid that is 30 cm wide at the bottom, 70 cm wide at the top, and has height 40 cm. If the trough is being filled with water at the rate of 0.1 m3/min how fast is the water level rising when ...
Sunday, March 30, 2014 at 6:43pm

Calculus
When dy/dx=(x-6)^½ what does y equal?
Saturday, March 29, 2014 at 4:11pm

Calculus
Jesse has constructed a huge cylindrical can with a diameter of 60 ft. The can is being filled with water at a rate of 450 ft3/min. How fast is the depth of the water increasing? (Hint: The volume of water in the cylinder is determined by πr2h where r is the radius and h ...
Friday, March 28, 2014 at 11:39pm

Calculus
At what interval is e^(-5x^2) concave up? I know the second derivative is 100x^2*e^-5x^2-10*e^-5x^2 but I just can not figure this one out. Thank you for your help!
Friday, March 28, 2014 at 7:38pm

Calculus
Find the area cut off by x=4 from the hyperbola x^2/9-y^2/4=1. Answer is 4.982 in the book. I have proceeded as under: Y=2/3*sqrt(x^2-9) and rhe reqd. area is double of integral 2/3*sqrt(x^2-9) from 3 to 4. Int= 2/3*[xsqrt(x^2-9)/2 – 9/2*log{x+sqrt(x^2-9)}] from 3 to 4 =x...
Friday, March 28, 2014 at 2:17am

Calculus Help Please!!!
In a murder investigation, the temperature of the corpse was 32.5 C at 1:30pm and 30.3 C an hour later. Normal body temperature is 37.0 C and the temperature of the surrounding was 20.0 C. When did the murder take place? PLEASE SHOW STEP BY STEP
Thursday, March 27, 2014 at 8:16pm

Calculus
A weight oscillates in a vertical motion according to the position function y(t)=-5 cos(t). Assuming t≥0, when will the acceleration if the weight be zero for the first time?
Thursday, March 27, 2014 at 2:51pm

Calculus
An object in free fall has its distance from the ground measured by the function d(t)=-4.9t^2 +50, where d is in meters and t is in seconds. If gravity is the only acceleration affecting the object, what is gravity's constant value?
Thursday, March 27, 2014 at 2:37pm

Calculus
If y=cos x, what is y^(6) (x)?
Thursday, March 27, 2014 at 11:18am

CALCULUS problem
There are four parts to this one question, and would really appreciate if you could show and explain how you get to the answer, because I tried looking up how to find the answer myself, but nothing made sense. Thank you! 11. The region R is bounded by the x-axis, x = 1, x = 3...
Thursday, March 27, 2014 at 8:51am

Calculus
Posted by MG on Wednesday, March 26, 2014 at 6:54pm. The hands of a clock in some tower are 4.5m and 2m in length. How fast is the distance between the tips of the hands changing at 9:00? (Hint: Use the law of cosines) The distance between the tips of the hands is changing at ...
Thursday, March 27, 2014 at 3:36am

Calculus
If e^x = 243 and e^y = 32 then e^((3x + 4y)/5) =? The answer is 432, but I don't understand why.
Thursday, March 27, 2014 at 3:34am

pre calculus
A taxi company charges $2.00 for the first mile (or part of a mile) and 20 cents for each succeeding tenth of a mile (or part). Express the cost C (in dollars) of a ride as a piecewise-defined function of the distance x traveled (in miles) for 0 < x < 2
Thursday, March 27, 2014 at 12:07am

Calculus
The height in feet above the ground of a ball thrown upwards from the top of a building is given by s=-16t^2 + 160t + 200, where t is the time in seconds. If the maximum height is 600 feet, what is v^-1(32)? The answer is supposed to be 4 seconds, but I don't understand ...
Wednesday, March 26, 2014 at 11:07pm

Calculus
You are given a piece of sheet metal that is twice as long as it is wide an has an area of 800m^2. Find the dimensions of the rectangular box that would contain a max volume if it were constructed from this piece of metal by cutting out squares of equal area at all four ...
Wednesday, March 26, 2014 at 9:49pm

Calculus
Use a tangent line approximation at x=0 to estimate the value of sin(-0.1). I got 0.1
Wednesday, March 26, 2014 at 8:56pm

Calculus
The vertical position of an object is modeled by the function h(t)=-16t^2 +5t+7, where h is measured in feet and t is measured in seconds. Find the object's initial velocity (that is, the velocity at t=0). Is it 5 feet per second?
Wednesday, March 26, 2014 at 8:46pm

Pre calculus
For the most part, will a law of cosines always be one triangle? As in one triangle to solve?
Wednesday, March 26, 2014 at 8:35pm

College Calculus
The hands of a clock in some tower are 4.5m and 2m in length. How fast is the distance between the tips of the hands changing at 9:00? (Hint: Use the law of cosines) The distance between the tips of the hands is changing at a rate of _______ m/hr at 9:00? I tried several times...
Wednesday, March 26, 2014 at 6:54pm

Calculus
If position is given by p(t)=t^2 +1, find the velocity v(t) at t = 2. I'm completely lost as to where to even start with this problem.
Wednesday, March 26, 2014 at 4:25pm

Calculus
The amount of carbon-14 still present in a sample after t years is given by the function where C0 is the initial amount. Estimate the age of a sample of wood discovered by an archeologist if the carbon level in the sample is only 18% of its original carbon-14 level.
Wednesday, March 26, 2014 at 10:31am

Calculus
If 40 milligrams of strontium-90 radioactively decays to 12 milligrams in 30 years, find its half-life (the number of years it takes until half of it remains). Use the formula A = p ⋅ e−kt, where p is the amount and A the (smaller) final amount.
Wednesday, March 26, 2014 at 10:29am

pre calculus
Find the exact values: tan(7pi/4) - tan (pi/6)
Wednesday, March 26, 2014 at 1:42am

Calculus
Find a positive number such that the sum of the square of the number and its reciprocal is a minimum.
Tuesday, March 25, 2014 at 9:25pm

Grade 12 Calculus
For an outdoor concert, a ticket price of $30 typically attracts 5000 people. For each $1 increase in the ticket price, 100 fewer people will attend. The revenue, R, is the product of the number of people attending and the price per ticket. a) Let x represent the number of $1 ...
Tuesday, March 25, 2014 at 8:46pm

Calculus
There are 50 apple trees in an orchard, and each tree produces an average of 200 apples each year. For each additional tree planted within the orchard, the average number of apples produced drops by 5. What is the optimal number of trees to plant in the orchard? I mostly need ...
Tuesday, March 25, 2014 at 8:09pm

Grade 12 Calculus
A rectangular piece of paper with perimeter 100 cm is to be rolled to form a cylindrical tube. Find the dimensions of the paper that will produce a tube with maximum volume. I have made it up to getting an equation for V(w).
Tuesday, March 25, 2014 at 7:49pm

Calculus Rate of Change
Find the average rate of change h(x)=2x^2-4 from x=2 to x=6 Simplify your answer as much as possible
Tuesday, March 25, 2014 at 10:27am

calculus
Recall that the volume of a sphere of radius r is V(r) =4\, \pi\, r^3 /3. Find L, the linearisation of V(r) at r=50
Tuesday, March 25, 2014 at 2:05am

Calculus A
Find all relative extrema and points of inflection for the function; h(x)=(x^2+5x+4)/(x-1)
Monday, March 24, 2014 at 11:20pm

Calculus
Find dy/dx implicitly in terms of x and y only for the following function; x+ 4xy=y^2
Monday, March 24, 2014 at 11:17pm

Calculus A
Find all relative extrema and points of inflection for the following function... h(X)= X^2+5X+4/ X-1 min= max= inflection points=
Monday, March 24, 2014 at 7:16pm

calculus
Suppose that a particle moves along a line so that its velocity v at time t is given by this piecewise function: v(t)=5t if 0≤t<1 v(t)=6((t)^(1/2))-(1/t) if 1≤t where t is in seconds and v is in centimeters per second (cm/s). Estimate the time(s) at which the ...
Sunday, March 23, 2014 at 8:17pm

Calculus
Find the slope of the tangent line to the ellipse x^2/4 + y^2/16= 1 at the point (x,y)
Sunday, March 23, 2014 at 8:11pm

Calculus
Suppose you have a hot cup of coffee in a room where the temp is 45 Celcius. Let y(t) represent the temp. of coffee as a function of the number of minutes t that have passed since the coffee was poured a) write a differential equation that applies to newtons law of cooling. ...
Sunday, March 23, 2014 at 6:16pm

Calculus Help Please!!!
find y' and y” by implicit differentiation. 2x^3 + 3y^3 = 8
Saturday, March 22, 2014 at 3:53pm

Calculus
A rancher wants to build a rectangular fence next to a river, using 100 yd of fencing. What dimensions of the rectangle will maximize the area? What is the maximum area? (Note that the rancher should not fence the side next to the river.)
Saturday, March 22, 2014 at 5:45am

Calculus
A ball is thrown vertically upward with an initial velocity of 135 feet per second, the ball’s height after t second is s(t) = 135t – 22t How to calculate average velocity from 1 to 3 seconds?
Saturday, March 22, 2014 at 12:34am

Calculus
Evaluate the improper integral or state that it diverges: integral from -inf to inf (2xe^-x) dx. Please help!
Thursday, March 20, 2014 at 8:39pm

Calculus Help STEVE
find y'' by implicit differentiation. 2x^3 + 3y^3 = 8 I got the first derivative as you but the problem was asking for second derivative by implicit diff. this is where i got confused. Thank you!!!
Thursday, March 20, 2014 at 5:51pm

Calculus Help
find y'' by implicit differentiation. 2x^3 + 3y^3 = 8
Thursday, March 20, 2014 at 3:28pm

Calculus Help Please!!!
find the derivative of the function. Simplify where possible. F(theta)=arcsin(square root of (sin9(theta)))
Thursday, March 20, 2014 at 2:42pm

CALCULUS HELP
Let r(x)= f(g(h(x))), where h(1)=4, g(4)=5, h'(1)=3 , g'(4)=5 and f'(5)=7. find r'(1).
Thursday, March 20, 2014 at 2:04pm

Calculus Help Please!!!
Find an equation of the tangent line to the curve at the given point. ((pi/6),(2 square root of (3)/3)) y = sec (x)
Thursday, March 20, 2014 at 1:54pm

Calculus :(
Differentiate with respect to (t). y = d cos(t) + (t^2)sin(t)
Thursday, March 20, 2014 at 1:52pm

calculus
Evaluate the improper integral or state that it diverges: integral from 6 to infinity (1/t^2-5t)dt. I need help on solving this and what does it mean by converges and diverges?
Thursday, March 20, 2014 at 2:10am

Calculus Help
use logarithmic diff. to find the derivative of the function. Show steps please! so I can see how it is done. Thank you so much! y=(e^(-x)cos^(2)(x))/(x^(2)+x+1)
Tuesday, March 18, 2014 at 10:47pm

AP Calculus
Approximating the integral from 0 to 6 of (e^x dx) by 3 circumscribed rectangles of equal width on the x-axis yields ____. a) 2e^2 + 4e^4 + 6e^6 b) 2(e^2 + e^4 + e^6) c) 2(e + e^3 + e^5) d) e + 3e^3 + 5e^5 e) e^2 + 3e^4 + 5e^6
Monday, March 17, 2014 at 4:40pm

Calculus Help
Use logarithmic differentiation to find the derivative of the function. y = (tan x)^(7/x)
Sunday, March 16, 2014 at 7:43pm

Calculus
Solve the initial-value problem. y'' - 2y' + y = 0 , y(2) = 0 , y'(2) = 1
Sunday, March 16, 2014 at 6:40pm

Calculus
Solve the boundary-value problem. y'' + 5y' - 6y = 0 , y(0) = 0 , y(2) = 1
Sunday, March 16, 2014 at 6:39pm

AP Calculus
The average area of all squares with sides between a inches and b inches (b>a) is ____ in^2.
Sunday, March 16, 2014 at 6:14pm

AP Calculus
The base of a solid is bounded by y =|x|+a, 0<a<3, and the line y=3. find in cu. units in terms of a, the volume of the solid if every cross section perpendicular to the y-axis is an equilateral triangle.
Sunday, March 16, 2014 at 6:13pm

Calculus Help
Use logarithmic differentiation to find the derivative of the function. show steps please! y=(e^-xcos^2(x))/(x^2+x+1)
Sunday, March 16, 2014 at 4:12pm

Calculus Help Please!!!
Use implicit diff. to find dy/dx of each of the following. In the following x,y and (a) are all variables. Show step by step please! Thank you! 1) y^2 = x^2+a^2 2) y^2+ay = x^2+ax+a^2
Sunday, March 16, 2014 at 3:54pm

calculus
using the method of shells, set up, but dont evaluate the integral, an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Y=e^x, x=0, y=2, about y=1
Sunday, March 16, 2014 at 2:30pm

Pre-Calculus
Express the complex number in polar form. 5-12i
Saturday, March 15, 2014 at 6:51pm

Pre-Calculus
Find this quotient. Express the result in rectangular form. 9(cos3π/2 + isin3π/2) ÷ 3(cosπ/4 + isinπ/4)
Saturday, March 15, 2014 at 6:49pm

Pre-Calculus
Express the number in rectangular form. 3(cosπ/3+isinπ/3)
Saturday, March 15, 2014 at 6:40pm

Pre Calculus
Find each product or quotient. Express the result in rectangular form. 2(cosπ/6+isinπ/6) X 4(cos2π/3 +i2π/3)
Saturday, March 15, 2014 at 6:39pm

Calculus
Find equations of both the tangent lines to the ellipse x^2 + 4y^2 = 36 that pass through the point (12, 3). smaller slope y= larger slope y=
Friday, March 14, 2014 at 5:24pm

Calculus Help and Check
Find dy/dx by implicit differentiation. x^5(x + y) = y^2(9x − y) this is what i've got so far but I dont think it is the right answer. y'= 9y^2-6x^5-5x^3y/x^5+9y^2-18xy
Friday, March 14, 2014 at 3:53pm

Calculus
Find four other forms of the point (4, 105°) Two of the four must include a negative r value.
Friday, March 14, 2014 at 12:02am

Calculus Help
In the following x,y and (a) are all variables. Show steps please! Thank you! 1) y^2 = x^2+a^2 2) y^2+ay = x^2+ax+a^2
Thursday, March 13, 2014 at 8:19pm

CALCULUS ECONOMICS
Consider the problem of a competitive firm which has fixed costs of $1000, semi-fixed-costs of $1000, and variable costs given by q^2. QUESTION: What is the maximum market price at which the firm decides to supply zero?
Thursday, March 13, 2014 at 4:10pm

CALCULUS ECONOMICS
Consider the problem of a competitive firm which has fixed costs of $1000, semi-fixed-costs of $1000, and variable costs given by q2. QUESTION: What is the maximum market price at which the firm decides to supply zero?
Thursday, March 13, 2014 at 4:09pm

CALCULUS ECONOMICS
Consider a market in which consumption of the good being traded generates a positive externality. There are 100 identical consumers, each with a utility function given by (1/2)*(q^(1/2))+m +(G^(1/2)) where G denotes the total level of consumption in the market. The good is ...
Thursday, March 13, 2014 at 4:08pm

CALCULUS ECONOMICS
Consider a market in which consumption of the good being traded generates a positive externality. There are 100 identical consumers, each with a utility function given by (1/2)*(q^(1/2))+m +(G^(1/2)) where G denotes the total level of consumption in the market. The good is ...
Thursday, March 13, 2014 at 4:06pm

CALCULUS ECONOMICS
Consider an oligopolistic market with two firms. Each of them produces using a cost function given by c(q)=q^2. The aggregate demand in the market is given by 1000−p. Suppose that, in order to increase production, the government gives the firms a $100 per-unit produced ...
Thursday, March 13, 2014 at 3:58pm

CALCULUS ECONOMICS
Consider the same setting as in the previous question. Suppose that firms are NOT owned by consumers. Let s denote the size of the per-unit subsidy/tax given to the firms. Let positive values of s denote subsidies, and negative values of s denote taxes. QUESTION: What is the ...
Thursday, March 13, 2014 at 3:54pm

CALCULUS ECONOMICS
Consider an oligopolistic market with two firms. Each of them produces using a cost function given by c(q)=q^2. The aggregate demand in the market is given by 1000−p. Suppose that, in order to increase production, the government gives the firms a $100 per-unit produced ...
Thursday, March 13, 2014 at 3:53pm

CALCULUS ECONOMICS
Consider an economy in which a monopolistic firm serves two identical, but separate markets, called A and B. The aggregate inverse demand in each market is given by 1000−q. The cost function for the monopolist is given by (qA+qB)^2, where qA andqB denotes the amount sold...
Thursday, March 13, 2014 at 3:52pm

CALCULUS ECONOMICS
Consider a market in which aggregate demand is given by 1000−10p, and aggregate supply is given by 10p, where p denotes the market price. QUESTION: What is the maximum amount of revenue that the government can raise using a per-unit sales tax on consumers?
Thursday, March 13, 2014 at 3:50pm

CALCULUS ECONOMICS
Consider the problem of a rational consumer with an experienced utility function given by 8*x^(1/2)+m. Let p=$1 p/unit denote the market price of good x. Suppose that, initially, the firm selling the good matches his purchases as follows: for every x units that he buys, he ...
Thursday, March 13, 2014 at 3:49pm

CALCULUS ECONOMICS
Consider the problem of a rational consumer with an experienced utility function given by 8x√+m. Let p=$1 p/unit denote the market price of good x. Suppose that, initially, the firm selling the good matches his purchases as follows: for every x units that he buys, he ...
Thursday, March 13, 2014 at 3:47pm

Pre-Calculus
Write the polar equation in rectangular form... r=5sintheta
Thursday, March 13, 2014 at 3:28pm

Pre-Calculus
Find the polar coordinates of each point with the given rectangular coordinates. Use degrees. (-4,-3)
Thursday, March 13, 2014 at 3:25pm

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